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C73×D105 #29506451

order15330
isoclinismisoclinic class of D105
automorphism?
homologyAbelianization (H1) = C2×C73 · Schur multiplier (H2) = C1

Aliases

direct productC73×D105
unambiguous semidirect productC3⋊(D35×C73)
unambiguous semidirect productC5⋊(D21×C73)
unambiguous semidirect productC7⋊(D15×C73)

Splittings

Fitting, socle, HallC3×C5×C7×C73 ⋊ C2
derived, HallC3×C5×C7 ⋊ C2×C73
HallC5×C7×C73 ⋊ D3
HallC3×C7×C73 ⋊ D5
HallC3×C5×C73 ⋊ D7
HallC7×C73 ⋊ D15
HallC5×C73 ⋊ D21
HallC3×C73 ⋊ D35
HallC5×C7 ⋊ D3×C73
HallC3×C7 ⋊ D5×C73
HallC3×C5 ⋊ D7×C73
SylowC7 ⋊ D15×C73
SylowC5 ⋊ D21×C73
SylowC3 ⋊ D35×C73

Subgroups

subgroupG/H
center, hypercenterC73D105
commutator, cosocle, hypocenterC3×C5×C7C2×C73
FrattiniC1G
Fitting, socleC3×C5×C7×C73C2
LCSG ▷ C3×C5×C7
UCSC1 ◁ C73

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 7665

Conjugacy classes & character table

3942 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofD73×D105, D7×D15×C73, D511⋊D15, …
maximal normal subgroup ofD73×D105, D7×D15×C73, D511⋊D15, …
maximal quotient ofC73×Dic105, C2×C73×D105

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15330, 19);